This project will innovate statistical methods that resolve how the myriad microorganisms that comprise the human microbiome interact with one another and with their host. The human microbiome is an important contributor to health and physiology, but efforts to manage it are stifled by a limited understanding of how the microbiome operates. One common strategy towards resolving this operation is to use correlation-type analyses of organismal abundance to model the biological interactions among microbes or between microbes and their host. However, the underlying biological interactions are often masked by the co-occurrence patterns in a community: two microbes that independently interact with a third, but not with one another, may appear to correlate. Additionally, existing methods fail to account for specific properties of microbiome data, including its heterogeneous compositional count nature, the complex environmental context, and its evolutionary structure. This project will develop statistical methods built on conditional dependencies that disentangle biological interactions from marginal correlations to produce mechanistically and evolutionarily relevant network models of how microbes interact with one another and their host. Specifically, it will (1) establish statistical methods that incorporate unique features in microbiome data to detect biological interactions, (2) advance graphical models for data integration to estimate how microbiota interact with paired 'omics data (e.g., metabolomics) and infer the phylogenetic redundancy of these interactions, and (3) create a new statistical regularization framework to quantify how host variation impacts the topology of microbial interaction networks. The methods and software produced by this work will transform our understanding of how microbiomes operate and influence or respond to their host. As a result, this work will produce knowledge critical to long-term efforts to manage and engineer microbiomes with the goal of eliciting specific clinical or physiological processes. This work can also profoundly influence industry efforts to develop microbiome-related products such as clinical diagnostics, novel drugs, and therapeutic probiotics.